A unit scale is to be prepared whose length does not change with … - Vidyadip

MCQ

A unit scale is to be prepared whose length does not change with temperature and remains $20\,cm$, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is $40\,cm$ and length of iron will be$...cm$

$\left(\alpha_{\text {iron }}=1.2 \times 10^{-5} K ^{-1}\right.$ and $\left.\alpha_{\text {brass }}=1.8 \times 10^{-5} K ^{-1}\right)$.

A
$59$
B
$6$
✓
$60$
D
$600$

✓

Answer

Correct option: C.

$60$

c
$\ell_{ B }\left(1+\alpha_{ B } \Delta T \right)-\ell_{ i }\left(1+\alpha_{ i } \Delta T \right)=\ell_{ B }-\ell_{ i }$

$\alpha_{ B } \ell_{ B }=\ell_{ i } \alpha_{ i }$

$1.8 \times 10^{-5} \times 40=\ell_{ i } \times 1.2 \times 10^{-5}$

$\ell_{ i }=\frac{1.8 \times 10^{-5} \times 40}{1.2 \times 10^{-5}}=\frac{3 \times 40}{2}=60$ $\ell_{ i }=60\,cm$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 10.1, thermonetry,thermal expansion and calorimetry→10.1, thermonetry,thermal expansion and calorimetry — all question types→Physics STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

A block is kept on a fixed smooth wedge whose vertical section is a curve $y = \frac{{{x^2}}}{{\sqrt 3 }}$ as shown in figure where $x$ represents horizontal direction and $y$ represents vertical direction. When released from a point where $y = \frac{1}{{4\sqrt 3 }}$ , what will be its acceleration ? $(g \,= 10\, m/s^2)$ ....... $m/s^2$

A progressive wave travelling along the positive $x-$ direction is represented by $y(x, t) = A\,sin\,\left( {kx - \omega t + \phi } \right)$. Its snapshot at $t = 0$ is given in the figure For this wave, the phase $\phi $ is

A ball is thrown up in the sky. After reaching a height, the ball falls back. What can be said about the average velocity?

A body of mass $\mathrm{m}=10\; \mathrm{kg}$ is attached to one end of a wire of length $0.3\; \mathrm{m} .$ The maximum angular speed (in $rad \;s^{-1}$ ) with which it can be rotated about its other end in space station is (Breaking stress of wire $=4.8 \times 10^{7} \;\mathrm{Nm}^{-2}$ and area of cross-section of the wire $=10^{-2}\; \mathrm{cm}^{2}$ ) is

A constant torque acting on a uniform circular wheel changes its angular momentum from $A_0$ to $4A_0$ in $4\, second$. The magnitude of this toque is

The magnetic field energy in an inductor changes from maximum value to minimum value in 5.0ms when connected to an AC source. The frequency of the source:

20Hz.
50Hz.
200Hz.
500Hz.

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is $v$. For a satellite orbiting at an altitude of half of the earth's radius, the orbital velocity is

A ball of mass $0.2\, kg$ moves with a velocity of $20 \,m/sec$ and it stops in $0.1 \,sec$; then the force on the ball is ........... $N$

According to Newtonl's law of cooling, the rate of cooling is :

The general motion of a rigid body can be considered to be a combination of $(i)$ a motioon --- centre of mass about an axis, and $(ii)$ its motion about an instantanneous axis passing through center of mass. These axes need not be stationary. Consider, for example, a thin uniform welded (rigidly fixed) horizontally at its rim to a massless stick, as shown in the figure. Where disc-stick system is rotated about the origin ona horizontal frictionless plane with angular sp--- $\omega$, the motion at any instant can be taken as a combination of $(i)$ a rotation of the centre of mass the disc about the $z$-axis, and $(ii)$ a rotation of the disc through an instantaneous vertical axis pass through its centre of mass (as is seen from the changed orientation of points $P$ and $Q$). Both the motions have the same angular speed $\omega$ in the case. $Image$ Now consider two similar systems as shown in the figure: case $(a)$ the disc with its face ver--- and parallel to $x - z$ plane; Case $(b)$ the disc with its face making an angle of $45^{\circ}$ with $x$-y plane its horizontal diameter parallel to $x$-axis. In both the cases, the disc is weleded at point $P$, and systems are rotated with constant angular speed $\omega$ about the $z$-axis.$Image$

$1.$ Which of the following statement regarding the angular speed about the istantaneous axis (passing through the centre of mass) is correct?

$(A)$ It is $\sqrt{2} \omega$ for boht the cases

$(B)$ it is $\omega$ for case $(a)$; and $\frac{w}{\sqrt{2}}$ for case $(b)$.

$(C)$ It is $\omega$ for case $(a)$; and $\sqrt{2} \omega$ for case $(b)$.

$(D)$ It is $\omega$ for both the cases

$2.$ Which of the following statements about the instantaneous axis (passing through the centre of mass) is correct?

$(A)$ It is vertical for both the cases $(a)$ and $(b)$.

$(B)$ It is verticle for case $(a)$; and is at $45^{\circ}$ to the $x-z$ plane and lies in the plane of the disc for case $(b)$

$(C)$ It is horizontal ofr case $(a)$; and is at $45^{\circ}$ to the $x - z$ plane and is normal to the plane of the disc for case $(b)$.

$(D)$ It is vertical of case $(a)$; and is at $45^{\circ}$ to the $x - z$ plane and is normal to the plane of the disc for case $(b)$.

Give the answer question $1$ and $2.$